Consider in the following the timelike hyperboloids defined by the condition
\(\zeta =\zeta _\bullet \)  where \(\zeta _\bullet \)  is a constant.
The key observation in [1]} is that although the conformal
metric (REF ) is singular at
\(\zeta =0\) ,
the conformal 3-metric
\({{\mathbf {q}}} = H^2 \tilde{{\mathbf {q}}} ={\mathbf {\ell }}\) 
